Modularity reflects the strength of division of a network into communities [1]}, i.e., a network with a high modularity indicates that nodes are densely connected within the communities and sparsely connected across different communities. Thus, we explore the relationship between modularity and network structural difference. We define the community segmentation with the maximal network modularity as \(Q\) , which corresponds to the optimal division of a network [2]}. Given two networks \(G_1\)  and \(G_2\) , we define the modularity difference between them as \(\Delta Q\)  = \(\left|Q_1 - Q_2\right|\) . Figure REF  shows the correlation between \(\Delta Q\)  and dissimilarity value \(D_{NE}\)  on 12 real networks. The result shows that the similar networks tend to have small value of \(\Delta Q\)  and vice verse. It further emphasizes the good performance of our network embedding based network comparison method.
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